Creating a transparency mask using a texture and blending with shaders
I think I can point you in the right direction.

You need to define a wave texture and apply it along a gradient, so we'll need a wave texture node, and if you use a separate XYZ node you should be able to find a direction that gives you the gradient you need.  For this object it's the Z axis.

I'm going to use a Color Ramp to invert the Z gradient and give us a little more control if we choose to exercise it, a Math node to bump up the value, and then subtract out the wave texture.  I've clamped the last operation, but maybe it's not necessary.

If we use this map as the factor of a mix shader between the blue emission and a transparent BSDF, we can assemble the rest of your shader behind it and we get very close to your desired effect.

From here I think you can find something you like.  The way I chose to do this was to animate a 4d noise texture mixed into the coordinate space, and then move the minkowski voronoi texture along the Z axis.